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The correct answer is option 4, Shah Alam II. Shah Alam II was the Mughal Emperor who granted the Dewani (revenue collection rights) of Bengal to the British East India Company in the year 1765.
Option 1, Jehangir, is incorrect as he was not the emperor who granted the Dewani of Bengal to the British East India Company.
Option 2, Shah Jahan, is also incorrect as he reigned from 1628 to 1658, which is much earlier than the year 1765 when the Dewani of Bengal was granted.
Option 3, Aurangzeb, is also incorrect as he reigned from 1658 to 1707, again much earlier than the year 1765 when the Dewani of Bengal was granted.
Therefore, the correct answer is option 4, Shah Alam II, as he was the Mughal Emperor who granted the Dewani of Bengal to the British East India Company in the year 1765.